In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length l.Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room.A small jerk wave pulse is given at the end 'C'.It goes up to upper end 'A' in time 't' .If the value of t is given by `a sqrt(l/g)+b sqrt(l/g)(sqrtc-sqrtd)` then a+b+c+d is

Options

A. `(620)/(670)s`
B. `(434)/(205)s`
C. 2s
D. None of thse

Answer

C

Explanation

We use `v_(c) = sqrt(gx)`
` underset(0)overset(l)(int)(dx)/(sqrt(x)) = underset(0)overset(BC)(int)sqrt(g)dt`
`2sqrt(l) = g t_(BC)`
`t_(BC)` = `2sqrt((l)/(g))`
`v_(AB) = sqrt(((2m + (m)/(l)x)g)/(m/l)) = sqrt((2 + (x)/(l))gl)`
`underset(0)overset(l)(int)(dx)/(sqrt(2+(x)/(l))) = underset(0)overset(AB)(int)sqrt(gl) dt`
`2lsqrt(2 + (x)/(l)) = sqrt(gl) t_(ab)`
`2l(sqrt(3) -sqrt(2)) = sqrt(gl) t_(AB)`
`t_(AB) = 2(sqrt(3) - sqrt(2)) sqrt((l)/(g))`
`t = t_(BC) = t_(AB) = 2sqrt((l)/(g))(l + sqrt(3) - sqrt(2))`
`1.3 xx 2sqrt((961)/(1181) ) = 2.6 xx(31)/(41) = 1.96 cong2s`